For your own personal development, yes, it is worth writing the paper. Ask a local professor to evaluate it and give you feedback on it.
It can be submitted to a journal, but would only be accepted if it is sufficiently "novel" to appeal to other mathematicians. It is a fairly steep hurdle, but an experienced local professor can advise you there.
Note, however, that there are some journals dedicated to publishing student work. The need for a "wow" factor is a bit less there so it has a better chance of publication.
But writing the paper will help you firm and clarify the ideas. Learning, through practice, to be a clear writer in your field is a necessary step and the experience gives you some skill that will be important later. Have fun. Good luck.
Note also that almost all work in mathematics is based on earlier work. The exceptions are rare.